论文标题
零熵组的零熵动作不是主导的
Zero entropy actions of amenable groups are not dominant
论文作者
论文摘要
如果概率措施保留离散的$ g $的行动，则据说如果它对自身的一般扩展是同构的，则占主导地位。最近，显示出$ g = \ mathbb {z} $，当且仅当它具有正熵且对于任何$ g $的情况下，就有一个动作是主导的，正面熵意味着优势。在本文中，我们表明，相反的内容也适用于任何$ g $，即零熵意味着不占主导地位。
A probability measure preserving action of a discrete amenable group $G$ is said to be dominant if it is isomorphic to a generic extension of itself. Recently, it was shown that for $G = \mathbb{Z}$, an action is dominant if and only if it has positive entropy and that for any $G$, positive entropy implies dominance. In this paper, we show that the converse also holds for any $G$, i.e. that zero entropy implies non-dominance.
